LMFDB - Embedded newform 1008.2.q.k.529.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(529,1008)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1008.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.1
Character	$\chi$	$=$	1008.529
Dual form			1008.2.q.k.625.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73195 + 0.0184869i) q^{3} +(0.790938 - 1.36994i) q^{5} +(-2.57645 - 0.601597i) q^{7} +(2.99932 - 0.0640368i) q^{9} +O(q^{10})$	\(q+(-1.73195 + 0.0184869i) q^{3} +(0.790938 - 1.36994i) q^{5} +(-2.57645 - 0.601597i) q^{7} +(2.99932 - 0.0640368i) q^{9} +(2.58569 + 4.47855i) q^{11} +(-0.681985 - 1.18123i) q^{13} +(-1.34454 + 2.38730i) q^{15} +(-2.30781 + 3.99724i) q^{17} +(-0.0321742 - 0.0557274i) q^{19} +(4.47341 + 0.994307i) q^{21} +(3.37197 - 5.84043i) q^{23} +(1.24883 + 2.16305i) q^{25} +(-5.19349 + 0.166357i) q^{27} +(4.70787 - 8.15427i) q^{29} +2.66278 q^{31} +(-4.56109 - 7.70884i) q^{33} +(-2.86196 + 3.05376i) q^{35} +(0.880766 + 1.52553i) q^{37} +(1.20300 + 2.03323i) q^{39} +(-0.858924 - 1.48770i) q^{41} +(5.12012 - 8.86831i) q^{43} +(2.28455 - 4.15955i) q^{45} -5.20834 q^{47} +(6.27616 + 3.09997i) q^{49} +(3.92312 - 6.96569i) q^{51} +(-0.479996 + 0.831377i) q^{53} +8.18049 q^{55} +(0.0567545 + 0.0959224i) q^{57} +9.33353 q^{59} +14.3902 q^{61} +(-7.76611 - 1.63939i) q^{63} -2.15763 q^{65} +12.4981 q^{67} +(-5.73213 + 10.1777i) q^{69} +4.49160 q^{71} +(-0.941655 + 1.63099i) q^{73} +(-2.20291 - 3.72320i) q^{75} +(-3.96762 - 13.0943i) q^{77} -6.53504 q^{79} +(8.99180 - 0.384134i) q^{81} +(5.08661 - 8.81026i) q^{83} +(3.65066 + 6.32314i) q^{85} +(-8.00306 + 14.2098i) q^{87} +(-4.12369 - 7.14243i) q^{89} +(1.04647 + 3.45366i) q^{91} +(-4.61181 + 0.0492266i) q^{93} -0.101791 q^{95} +(-7.26638 + 12.5857i) q^{97} +(8.04210 + 13.2670i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 2 q^{3} + 3 q^{5} + 5 q^{7} + 10 q^{9}+O(q^{10}) $ 22 * q - 2 * q^3 + 3 * q^5 + 5 * q^7 + 10 * q^9	$ 22 q - 2 q^{3} + 3 q^{5} + 5 q^{7} + 10 q^{9} + 3 q^{11} - 3 q^{13} + q^{15} + 7 q^{17} + q^{19} - 2 q^{23} - 10 q^{25} + 4 q^{27} + 9 q^{29} - 8 q^{31} + 29 q^{33} - 14 q^{35} + 2 q^{37} + 16 q^{39} + 16 q^{41} + q^{45} + 10 q^{47} + 15 q^{49} - 7 q^{51} + 11 q^{53} - 22 q^{55} + 7 q^{57} - 38 q^{59} + 26 q^{61} - 48 q^{63} - 26 q^{65} + 52 q^{67} - 4 q^{69} + 48 q^{71} - 35 q^{73} + 23 q^{75} + 17 q^{77} + 20 q^{79} - 38 q^{81} + 28 q^{83} - 20 q^{85} + 33 q^{87} + 6 q^{89} + 37 q^{91} + 19 q^{93} + 24 q^{95} - 29 q^{97} + 56 q^{99}+O(q^{100}) $ 22 * q - 2 * q^3 + 3 * q^5 + 5 * q^7 + 10 * q^9 + 3 * q^11 - 3 * q^13 + q^15 + 7 * q^17 + q^19 - 2 * q^23 - 10 * q^25 + 4 * q^27 + 9 * q^29 - 8 * q^31 + 29 * q^33 - 14 * q^35 + 2 * q^37 + 16 * q^39 + 16 * q^41 + q^45 + 10 * q^47 + 15 * q^49 - 7 * q^51 + 11 * q^53 - 22 * q^55 + 7 * q^57 - 38 * q^59 + 26 * q^61 - 48 * q^63 - 26 * q^65 + 52 * q^67 - 4 * q^69 + 48 * q^71 - 35 * q^73 + 23 * q^75 + 17 * q^77 + 20 * q^79 - 38 * q^81 + 28 * q^83 - 20 * q^85 + 33 * q^87 + 6 * q^89 + 37 * q^91 + 19 * q^93 + 24 * q^95 - 29 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.73195	+	0.0184869i	−0.999943	+	0.0106734i
$3$	−1.73195	+	0.0184869i	−0.999943	+	0.0106734i
$4$		0			0
$5$	0.790938	−	1.36994i	0.353718	−	0.612658i	−0.633180	−	0.774005i	$-0.718251\pi$
$5$	0.790938	−	1.36994i	0.353718	−	0.612658i	0.986898	+	0.161347i	$0.0515839\pi$
$6$		0			0
$7$	−2.57645	−	0.601597i	−0.973806	−	0.227382i
$7$	−2.57645	−	0.601597i	−0.973806	−	0.227382i
$8$		0			0
$9$	2.99932	−	0.0640368i	0.999772	−	0.0213456i
$10$		0			0
$11$	2.58569	+	4.47855i	0.779616	+	1.35033i	0.932163	+	0.362038i	$0.117919\pi$
$11$	2.58569	+	4.47855i	0.779616	+	1.35033i	−0.152548	+	0.988296i	$0.548748\pi$
$12$		0			0
$13$	−0.681985	−	1.18123i	−0.189149	−	0.327615i	0.755818	−	0.654782i	$-0.227239\pi$
$13$	−0.681985	−	1.18123i	−0.189149	−	0.327615i	−0.944967	+	0.327167i	$0.893906\pi$
$14$		0			0
$15$	−1.34454	+	2.38730i	−0.347159	+	0.616398i
$16$		0			0
$17$	−2.30781	+	3.99724i	−0.559726	+	0.969473i	0.437794	+	0.899076i	$0.355760\pi$
$17$	−2.30781	+	3.99724i	−0.559726	+	0.969473i	−0.997519	+	0.0703975i	$0.977573\pi$
$18$		0			0
$19$	−0.0321742	−	0.0557274i	−0.00738128	−	0.0127847i	0.862311	−	0.506379i	$-0.169016\pi$
$19$	−0.0321742	−	0.0557274i	−0.00738128	−	0.0127847i	−0.869692	+	0.493594i	$0.835683\pi$
$20$		0			0
$21$	4.47341	+	0.994307i	0.976177	+	0.216976i
$22$		0			0
$23$	3.37197	−	5.84043i	0.703105	−	1.21781i	−0.264266	−	0.964450i	$-0.585130\pi$
$23$	3.37197	−	5.84043i	0.703105	−	1.21781i	0.967371	−	0.253364i	$-0.0815370\pi$
$24$		0			0
$25$	1.24883	+	2.16305i	0.249767	+	0.432609i
$26$		0			0
$27$	−5.19349	+	0.166357i	−0.999487	+	0.0320154i
$28$		0			0
$29$	4.70787	−	8.15427i	0.874229	−	1.51421i	0.0166475	−	0.999861i	$-0.494701\pi$
$29$	4.70787	−	8.15427i	0.874229	−	1.51421i	0.857582	−	0.514348i	$-0.171966\pi$
$30$		0			0
$31$	2.66278			0.478250			0.239125	−	0.970989i	$-0.423139\pi$
$31$	2.66278			0.478250			0.239125	+	0.970989i	$0.423139\pi$
$32$		0			0
$33$	−4.56109	−	7.70884i	−0.793984	−	1.34194i
$34$		0			0
$35$	−2.86196	+	3.05376i	−0.483760	+	0.516180i
$36$		0			0
$37$	0.880766	+	1.52553i	0.144797	+	0.250796i	0.929297	−	0.369333i	$-0.120414\pi$
$37$	0.880766	+	1.52553i	0.144797	+	0.250796i	−0.784500	+	0.620129i	$0.787080\pi$
$38$		0			0
$39$	1.20300	+	2.03323i	0.192635	+	0.325578i
$40$		0			0
$41$	−0.858924	−	1.48770i	−0.134141	−	0.232340i	0.791128	−	0.611651i	$-0.209494\pi$
$41$	−0.858924	−	1.48770i	−0.134141	−	0.232340i	−0.925269	+	0.379311i	$0.876161\pi$
$42$		0			0
$43$	5.12012	−	8.86831i	0.780811	−	1.35240i	−0.150658	−	0.988586i	$-0.548139\pi$
$43$	5.12012	−	8.86831i	0.780811	−	1.35240i	0.931470	−	0.363819i	$-0.118527\pi$
$44$		0			0
$45$	2.28455	−	4.15955i	0.340560	−	0.620068i
$46$		0			0
$47$	−5.20834			−0.759715			−0.379857	−	0.925045i	$-0.624027\pi$
$47$	−5.20834			−0.759715			−0.379857	+	0.925045i	$0.624027\pi$
$48$		0			0
$49$	6.27616	+	3.09997i	0.896594	+	0.442853i
$50$		0			0
$51$	3.92312	−	6.96569i	0.549346	−	0.975392i
$52$		0			0
$53$	−0.479996	+	0.831377i	−0.0659325	+	0.114198i	−0.897107	−	0.441813i	$-0.854336\pi$
$53$	−0.479996	+	0.831377i	−0.0659325	+	0.114198i	0.831175	+	0.556011i	$0.187669\pi$
$54$		0			0
$55$	8.18049			1.10306
$56$		0			0
$57$	0.0567545	+	0.0959224i	0.00751732	+	0.0127052i
$58$		0			0
$59$	9.33353			1.21512			0.607561	−	0.794273i	$-0.292148\pi$
$59$	9.33353			1.21512			0.607561	+	0.794273i	$0.292148\pi$
$60$		0			0
$61$	14.3902			1.84248			0.921241	−	0.388993i	$-0.127177\pi$
$61$	14.3902			1.84248			0.921241	+	0.388993i	$0.127177\pi$
$62$		0			0
$63$	−7.76611	−	1.63939i	−0.978437	−	0.206544i
$64$		0			0
$65$	−2.15763			−0.267621
$66$		0			0
$67$	12.4981			1.52688			0.763441	−	0.645878i	$-0.223509\pi$
$67$	12.4981			1.52688			0.763441	+	0.645878i	$0.223509\pi$
$68$		0			0
$69$	−5.73213	+	10.1777i	−0.690067	+	1.22525i
$70$		0			0
$71$	4.49160			0.533055			0.266527	−	0.963827i	$-0.414124\pi$
$71$	4.49160			0.533055			0.266527	+	0.963827i	$0.414124\pi$
$72$		0			0
$73$	−0.941655	+	1.63099i	−0.110212	+	0.190893i	−0.915856	−	0.401507i	$-0.868486\pi$
$73$	−0.941655	+	1.63099i	−0.110212	+	0.190893i	0.805643	+	0.592401i	$0.201820\pi$
$74$		0			0
$75$	−2.20291	−	3.72320i	−0.254370	−	0.429919i
$76$		0			0
$77$	−3.96762	−	13.0943i	−0.452152	−	1.49223i
$78$		0			0
$79$	−6.53504			−0.735250			−0.367625	−	0.929974i	$-0.619829\pi$
$79$	−6.53504			−0.735250			−0.367625	+	0.929974i	$0.619829\pi$
$80$		0			0
$81$	8.99180	−	0.384134i	0.999089	−	0.0426815i
$82$		0			0
$83$	5.08661	−	8.81026i	0.558328	−	0.967052i	−0.439309	−	0.898336i	$-0.644777\pi$
$83$	5.08661	−	8.81026i	0.558328	−	0.967052i	0.997636	−	0.0687156i	$-0.0218901\pi$
$84$		0			0
$85$	3.65066	+	6.32314i	0.395970	+	0.685840i
$86$		0			0
$87$	−8.00306	+	14.2098i	−0.858018	+	1.52345i
$88$		0			0
$89$	−4.12369	−	7.14243i	−0.437110	−	0.757096i	0.560355	−	0.828252i	$-0.310665\pi$
$89$	−4.12369	−	7.14243i	−0.437110	−	0.757096i	−0.997465	+	0.0711559i	$0.977331\pi$
$90$		0			0
$91$	1.04647	+	3.45366i	0.109700	+	0.362042i
$92$		0			0
$93$	−4.61181	+	0.0492266i	−0.478223	+	0.00510456i
$94$		0			0
$95$	−0.101791			−0.0104436
$96$		0			0
$97$	−7.26638	+	12.5857i	−0.737789	+	1.27789i	0.215700	+	0.976460i	$0.430797\pi$
$97$	−7.26638	+	12.5857i	−0.737789	+	1.27789i	−0.953489	+	0.301428i	$0.902537\pi$
$98$		0			0
$99$	8.04210	+	13.2670i	0.808262	+	1.33339i
$100$		0			0
$101$	−3.12310	−	5.40937i	−0.310760	−	0.538252i	0.667767	−	0.744370i	$-0.267250\pi$
$101$	−3.12310	−	5.40937i	−0.310760	−	0.538252i	−0.978527	+	0.206118i	$0.933917\pi$
$102$		0			0
$103$	−2.88881	+	5.00357i	−0.284643	+	0.493016i	−0.972523	−	0.232809i	$-0.925208\pi$
$103$	−2.88881	+	5.00357i	−0.284643	+	0.493016i	0.687879	+	0.725825i	$0.258542\pi$
$104$		0			0
$105$	4.90033	−	5.34188i	0.478223	−	0.521314i
$106$		0			0
$107$	0.251126	+	0.434963i	0.0242773	+	0.0420494i	0.877909	−	0.478828i	$-0.158938\pi$
$107$	0.251126	+	0.434963i	0.0242773	+	0.0420494i	−0.853632	+	0.520877i	$0.825605\pi$
$108$		0			0
$109$	−2.37218	+	4.10874i	−0.227214	+	0.393546i	−0.956981	−	0.290149i	$-0.906295\pi$
$109$	−2.37218	+	4.10874i	−0.227214	+	0.393546i	0.729767	+	0.683696i	$0.239628\pi$
$110$		0			0
$111$	−1.55365	−	2.62587i	−0.147466	−	0.249236i
$112$		0			0
$113$	−1.11328	−	1.92825i	−0.104728	−	0.181395i	0.808899	−	0.587948i	$-0.200064\pi$
$113$	−1.11328	−	1.92825i	−0.104728	−	0.181395i	−0.913627	+	0.406553i	$0.866731\pi$
$114$		0			0
$115$	−5.33404	−	9.23883i	−0.497402	−	0.861526i
$116$		0			0
$117$	−2.12113	−	3.49922i	−0.196099	−	0.323503i
$118$		0			0
$119$	8.35067	−	8.91031i	0.765505	−	0.816806i
$120$		0			0
$121$	−7.87162	+	13.6340i	−0.715601	+	1.23946i
$122$		0			0
$123$	1.51512	+	2.56075i	0.136614	+	0.230895i
$124$		0			0
$125$	11.8604			1.06082
$126$		0			0
$127$	18.6057			1.65099			0.825494	−	0.564410i	$-0.190896\pi$
$127$	18.6057			1.65099			0.825494	+	0.564410i	$0.190896\pi$
$128$		0			0
$129$	−8.70386	+	15.4541i	−0.766332	+	1.36066i
$130$		0			0
$131$	6.77020	−	11.7263i	0.591515	−	1.02453i	−0.402514	−	0.915414i	$-0.631863\pi$
$131$	6.77020	−	11.7263i	0.591515	−	1.02453i	0.994029	−	0.109120i	$-0.0348032\pi$
$132$		0			0
$133$	0.0493698	+	0.162935i	0.00428090	+	0.0141282i
$134$		0			0
$135$	−3.87983	+	7.24637i	−0.333922	+	0.623668i
$136$		0			0
$137$	−6.87100	−	11.9009i	−0.587029	−	1.01676i	−0.994619	−	0.103599i	$-0.966964\pi$
$137$	−6.87100	−	11.9009i	−0.587029	−	1.01676i	0.407590	−	0.913165i	$-0.366369\pi$
$138$		0			0
$139$	−6.79328	−	11.7663i	−0.576198	−	0.998005i	−0.995910	−	0.0903476i	$-0.971202\pi$
$139$	−6.79328	−	11.7663i	−0.576198	−	0.998005i	0.419712	−	0.907657i	$-0.362131\pi$
$140$		0			0
$141$	9.02060	−	0.0962861i	0.759671	−	0.00810875i
$142$		0			0
$143$	3.52681	−	6.10861i	0.294927	−	0.510828i
$144$		0			0
$145$	−7.44726	−	12.8990i	−0.618461	−	1.07121i
$146$		0			0
$147$	−10.9273	−	5.25297i	−0.901270	−	0.433258i
$148$		0			0
$149$	−2.98033	+	5.16209i	−0.244158	+	0.422895i	−0.961895	−	0.273420i	$-0.911845\pi$
$149$	−2.98033	+	5.16209i	−0.244158	+	0.422895i	0.717736	+	0.696315i	$0.245178\pi$
$150$		0			0
$151$	4.27071	+	7.39709i	0.347546	+	0.601967i	0.985813	−	0.167848i	$-0.0536819\pi$
$151$	4.27071	+	7.39709i	0.347546	+	0.601967i	−0.638267	+	0.769815i	$0.720349\pi$
$152$		0			0
$153$	−6.66587	+	12.1368i	−0.538904	+	0.981200i
$154$		0			0
$155$	2.10610	−	3.64786i	0.169166	−	0.293004i
$156$		0			0
$157$	−2.63992			−0.210688			−0.105344	−	0.994436i	$-0.533594\pi$
$157$	−2.63992			−0.210688			−0.105344	+	0.994436i	$0.533594\pi$
$158$		0			0
$159$	0.815960	−	1.44878i	0.0647099	−	0.114896i
$160$		0			0
$161$	−12.2013	+	13.0190i	−0.961597	+	1.02604i
$162$		0			0
$163$	8.87875	+	15.3785i	0.695438	+	1.20453i	0.970033	+	0.242973i	$0.0781228\pi$
$163$	8.87875	+	15.3785i	0.695438	+	1.20453i	−0.274595	+	0.961560i	$0.588544\pi$
$164$		0			0
$165$	−14.1682	+	0.151232i	−1.10299	+	0.0117734i
$166$		0			0
$167$	−3.98937	−	6.90979i	−0.308706	−	0.534695i	0.669373	−	0.742926i	$-0.266563\pi$
$167$	−3.98937	−	6.90979i	−0.308706	−	0.534695i	−0.978080	+	0.208231i	$0.933229\pi$
$168$		0			0
$169$	5.56979	−	9.64716i	0.428446	−	0.742090i
$170$		0			0
$171$	−0.100069	−	0.165084i	−0.00765250	−	0.0126243i
$172$		0			0
$173$	7.66341			0.582638			0.291319	−	0.956626i	$-0.405906\pi$
$173$	7.66341			0.582638			0.291319	+	0.956626i	$0.405906\pi$
$174$		0			0
$175$	−1.91627	−	6.32427i	−0.144857	−	0.478070i
$176$		0			0
$177$	−16.1652	+	0.172548i	−1.21505	+	0.0129695i
$178$		0			0
$179$	−11.7864	+	20.4147i	−0.880958	+	1.52586i	−0.0306808	+	0.999529i	$0.509768\pi$
$179$	−11.7864	+	20.4147i	−0.880958	+	1.52586i	−0.850277	+	0.526335i	$0.823566\pi$
$180$		0			0
$181$	17.3700			1.29110			0.645551	−	0.763717i	$-0.276628\pi$
$181$	17.3700			1.29110			0.645551	+	0.763717i	$0.276628\pi$
$182$		0			0
$183$	−24.9232	+	0.266031i	−1.84238	+	0.0196656i
$184$		0			0
$185$	2.78653			0.204869
$186$		0			0
$187$	−23.8691			−1.74548
$188$		0			0
$189$	13.4808	+	2.69578i	0.980586	+	0.196089i
$190$		0			0
$191$	−4.84660			−0.350687			−0.175344	−	0.984507i	$-0.556104\pi$
$191$	−4.84660			−0.350687			−0.175344	+	0.984507i	$0.556104\pi$
$192$		0			0
$193$	−14.6418			−1.05394			−0.526970	−	0.849884i	$-0.676672\pi$
$193$	−14.6418			−1.05394			−0.526970	+	0.849884i	$0.676672\pi$
$194$		0			0
$195$	3.73691	−	0.0398879i	0.267606	−	0.00285643i
$196$		0			0
$197$	−19.1996			−1.36791			−0.683957	−	0.729522i	$-0.739743\pi$
$197$	−19.1996			−1.36791			−0.683957	+	0.729522i	$0.739743\pi$
$198$		0			0
$199$	−6.50796	+	11.2721i	−0.461337	+	0.799060i	−0.999028	−	0.0440825i	$-0.985964\pi$
$199$	−6.50796	+	11.2721i	−0.461337	+	0.799060i	0.537691	+	0.843142i	$0.319297\pi$
$200$		0			0
$201$	−21.6460	+	0.231050i	−1.52679	+	0.0162970i
$202$		0			0
$203$	−17.0352	+	18.1768i	−1.19563	+	1.27576i
$204$		0			0
$205$	−2.71742			−0.189793
$206$		0			0
$207$	9.73961	−	17.7332i	0.676950	−	1.23254i
$208$		0			0
$209$	0.166385	−	0.288188i	0.0115091	−	0.0199344i
$210$		0			0
$211$	7.43389	+	12.8759i	0.511770	+	0.886412i	0.999907	+	0.0136450i	$0.00434348\pi$
$211$	7.43389	+	12.8759i	0.511770	+	0.886412i	−0.488137	+	0.872767i	$0.662323\pi$
$212$		0			0
$213$	−7.77923	+	0.0830357i	−0.533024	+	0.00568951i
$214$		0			0
$215$	−8.09940	−	14.0286i	−0.552374	−	0.956740i
$216$		0			0
$217$	−6.86052	−	1.60192i	−0.465722	−	0.108746i
$218$		0			0
$219$	1.60075	−	2.84221i	0.108169	−	0.192059i
$220$		0			0
$221$	6.29556			0.423485
$222$		0			0
$223$	−11.2085	+	19.4136i	−0.750574	+	1.30003i	0.196971	+	0.980409i	$0.436890\pi$
$223$	−11.2085	+	19.4136i	−0.750574	+	1.30003i	−0.947545	+	0.319623i	$0.896444\pi$
$224$		0			0
$225$	3.88417	+	6.40769i	0.258944	+	0.427179i
$226$		0			0
$227$	1.94725	+	3.37273i	0.129243	+	0.223856i	0.923384	−	0.383878i	$-0.125412\pi$
$227$	1.94725	+	3.37273i	0.129243	+	0.223856i	−0.794140	+	0.607735i	$0.792078\pi$
$228$		0			0
$229$	0.693586	−	1.20133i	0.0458334	−	0.0793858i	−0.842199	−	0.539167i	$-0.818739\pi$
$229$	0.693586	−	1.20133i	0.0458334	−	0.0793858i	0.888032	+	0.459782i	$0.152072\pi$
$230$		0			0
$231$	7.11379	+	22.6053i	0.468053	+	1.48732i
$232$		0			0
$233$	8.99057	+	15.5721i	0.588992	+	1.02016i	0.994365	+	0.106013i	$0.0338084\pi$
$233$	8.99057	+	15.5721i	0.588992	+	1.02016i	−0.405373	+	0.914151i	$0.632858\pi$
$234$		0			0
$235$	−4.11947	+	7.13514i	−0.268725	+	0.465445i
$236$		0			0
$237$	11.3184	−	0.120813i	0.735208	−	0.00784763i
$238$		0			0
$239$	2.68043	+	4.64264i	0.173382	+	0.300307i	0.939600	−	0.342274i	$-0.111197\pi$
$239$	2.68043	+	4.64264i	0.173382	+	0.300307i	−0.766218	+	0.642581i	$0.777864\pi$
$240$		0			0
$241$	−0.208296	−	0.360779i	−0.0134175	−	0.0232398i	0.859239	−	0.511575i	$-0.170938\pi$
$241$	−0.208296	−	0.360779i	−0.0134175	−	0.0232398i	−0.872656	+	0.488335i	$0.837604\pi$
$242$		0			0
$243$	−15.5663	+	0.831531i	−0.998576	+	0.0533428i
$244$		0			0
$245$	9.21084	−	6.14611i	0.588459	−	0.392661i
$246$		0			0
$247$	−0.0438847	+	0.0760106i	−0.00279232	+	0.00483644i
$248$		0			0
$249$	−8.64688	+	15.3530i	−0.547974	+	0.972956i
$250$		0			0
$251$	−22.5606			−1.42401			−0.712006	−	0.702173i	$-0.752213\pi$
$251$	−22.5606			−1.42401			−0.712006	+	0.702173i	$0.752213\pi$
$252$		0			0
$253$	34.8756			2.19261
$254$		0			0
$255$	−6.43967	−	10.8839i	−0.403268	−	0.681575i
$256$		0			0
$257$	5.52307	−	9.56624i	0.344520	−	0.596726i	−0.640747	−	0.767752i	$-0.721375\pi$
$257$	5.52307	−	9.56624i	0.344520	−	0.596726i	0.985266	+	0.171027i	$0.0547084\pi$
$258$		0			0
$259$	−1.35149	−	4.46032i	−0.0839776	−	0.277151i
$260$		0			0
$261$	13.5982	−	24.7587i	0.841708	−	1.53253i
$262$		0			0
$263$	−12.7310	−	22.0508i	−0.785028	−	1.35971i	−0.928982	−	0.370124i	$-0.879315\pi$
$263$	−12.7310	−	22.0508i	−0.785028	−	1.35971i	0.143954	−	0.989584i	$-0.454018\pi$
$264$		0			0
$265$	0.759294	+	1.31514i	0.0466430	+	0.0807881i
$266$		0			0
$267$	7.27407	+	12.2941i	0.445166	+	0.752388i
$268$		0			0
$269$	2.78957	−	4.83168i	0.170083	−	0.294593i	−0.768366	−	0.640011i	$-0.778930\pi$
$269$	2.78957	−	4.83168i	0.170083	−	0.294593i	0.938449	+	0.345419i	$0.112263\pi$
$270$		0			0
$271$	1.46645	+	2.53997i	0.0890806	+	0.154292i	0.907123	−	0.420866i	$-0.138274\pi$
$271$	1.46645	+	2.53997i	0.0890806	+	0.154292i	−0.818042	+	0.575158i	$0.804940\pi$
$272$		0			0
$273$	−1.87629	−	5.96224i	−0.113558	−	0.360851i
$274$		0			0
$275$	−6.45821	+	11.1859i	−0.389445	+	0.674538i
$276$		0			0
$277$	−11.0458	−	19.1320i	−0.663680	−	1.14953i	−0.979641	−	0.200756i	$-0.935660\pi$
$277$	−11.0458	−	19.1320i	−0.663680	−	1.14953i	0.315961	−	0.948772i	$-0.397673\pi$
$278$		0			0
$279$	7.98653	−	0.170516i	0.478141	−	0.0102085i
$280$		0			0
$281$	−2.81009	+	4.86721i	−0.167636	+	0.290354i	−0.937588	−	0.347748i	$-0.886947\pi$
$281$	−2.81009	+	4.86721i	−0.167636	+	0.290354i	0.769952	+	0.638101i	$0.220280\pi$
$282$		0			0
$283$	−21.3003			−1.26617			−0.633086	−	0.774082i	$-0.718212\pi$
$283$	−21.3003			−1.26617			−0.633086	+	0.774082i	$0.718212\pi$
$284$		0			0
$285$	0.176298	−	0.00188181i	0.0104430	−	0.000111469i
$286$		0			0
$287$	1.31798	+	4.34971i	0.0777977	+	0.256755i
$288$		0			0
$289$	−2.15195	−	3.72729i	−0.126585	−	0.219252i
$290$		0			0
$291$	12.3524	−	21.9322i	0.724108	−	1.28569i
$292$		0			0
$293$	14.1128	+	24.4440i	0.824477	+	1.42804i	0.902319	+	0.431070i	$0.141864\pi$
$293$	14.1128	+	24.4440i	0.824477	+	1.42804i	−0.0778418	+	0.996966i	$0.524803\pi$
$294$		0			0
$295$	7.38224	−	12.7864i	0.429811	−	0.744454i
$296$		0			0
$297$	−14.1738	−	22.8292i	−0.822448	−	1.32468i
$298$		0			0
$299$	−9.19854			−0.531966
$300$		0			0
$301$	−18.5269	+	19.7685i	−1.06787	+	1.13944i
$302$		0			0
$303$	5.50906	+	9.31103i	0.316487	+	0.534905i
$304$		0			0
$305$	11.3818	−	19.7138i	0.651719	−	1.12881i
$306$		0			0
$307$	2.41329			0.137734			0.0688669	−	0.997626i	$-0.478062\pi$
$307$	2.41329			0.137734			0.0688669	+	0.997626i	$0.478062\pi$
$308$		0			0
$309$	4.91078	−	8.71935i	0.279365	−	0.496026i
$310$		0			0
$311$	−9.53680			−0.540782			−0.270391	−	0.962751i	$-0.587153\pi$
$311$	−9.53680			−0.540782			−0.270391	+	0.962751i	$0.587153\pi$
$312$		0			0
$313$	32.6020			1.84277			0.921386	−	0.388650i	$-0.127058\pi$
$313$	32.6020			1.84277			0.921386	+	0.388650i	$0.127058\pi$
$314$		0			0
$315$	−8.38838	+	9.34247i	−0.472632	+	0.526389i
$316$		0			0
$317$	−3.09954			−0.174088			−0.0870438	−	0.996204i	$-0.527742\pi$
$317$	−3.09954			−0.174088			−0.0870438	+	0.996204i	$0.527742\pi$
$318$		0			0
$319$	48.6924			2.72625
$320$		0			0
$321$	−0.442979	−	0.748692i	−0.0247247	−	0.0417879i
$322$		0			0
$323$	0.297008			0.0165260
$324$		0			0
$325$	1.70337	−	2.95033i	0.0944862	−	0.163655i
$326$		0			0
$327$	4.03255	−	7.16000i	0.223001	−	0.395949i
$328$		0			0
$329$	13.4190	+	3.13332i	0.739814	+	0.172746i
$330$		0			0
$331$	3.67650			0.202079			0.101039	−	0.994882i	$-0.467783\pi$
$331$	3.67650			0.202079			0.101039	+	0.994882i	$0.467783\pi$
$332$		0			0
$333$	2.73939	+	4.51915i	0.150117	+	0.247648i
$334$		0			0
$335$	9.88519	−	17.1216i	0.540086	−	0.935456i
$336$		0			0
$337$	6.15866	+	10.6671i	0.335483	+	0.581074i	0.983578	−	0.180486i	$-0.0577670\pi$
$337$	6.15866	+	10.6671i	0.335483	+	0.581074i	−0.648094	+	0.761560i	$0.724434\pi$
$338$		0			0
$339$	1.96379	+	3.31906i	0.106658	+	0.180266i
$340$		0			0
$341$	6.88514	+	11.9254i	0.372851	+	0.645797i
$342$		0			0
$343$	−14.3053	−	11.7626i	−0.772412	−	0.635122i
$344$		0			0
$345$	9.40910	+	15.9026i	0.506569	+	0.856168i
$346$		0			0
$347$	17.7016			0.950269			0.475135	−	0.879913i	$-0.342399\pi$
$347$	17.7016			0.950269			0.475135	+	0.879913i	$0.342399\pi$
$348$		0			0
$349$	0.562639	−	0.974519i	0.0301174	−	0.0521648i	−0.850574	−	0.525856i	$-0.823745\pi$
$349$	0.562639	−	0.974519i	0.0301174	−	0.0521648i	0.880691	+	0.473691i	$0.157079\pi$
$350$		0			0
$351$	3.73839	+	6.02127i	0.199540	+	0.321391i
$352$		0			0
$353$	5.48125	+	9.49381i	0.291738	+	0.505304i	0.974221	−	0.225597i	$-0.0724332\pi$
$353$	5.48125	+	9.49381i	0.291738	+	0.505304i	−0.682483	+	0.730901i	$0.739100\pi$
$354$		0			0
$355$	3.55257	−	6.15324i	0.188551	−	0.326580i
$356$		0			0
$357$	−14.2982	+	15.5866i	−0.756743	+	0.824930i
$358$		0			0
$359$	13.4733	+	23.3364i	0.711092	+	1.23165i	0.964448	+	0.264274i	$0.0851324\pi$
$359$	13.4733	+	23.3364i	0.711092	+	1.23165i	−0.253356	+	0.967373i	$0.581534\pi$
$360$		0			0
$361$	9.49793	−	16.4509i	0.499891	−	0.865837i
$362$		0			0
$363$	13.3812	−	23.7590i	0.702331	−	1.24703i
$364$		0			0
$365$	1.48958	+	2.58003i	0.0779682	+	0.135045i
$366$		0			0
$367$	17.4137	+	30.1614i	0.908986	+	1.57441i	0.815475	+	0.578792i	$0.196476\pi$
$367$	17.4137	+	30.1614i	0.908986	+	1.57441i	0.0935112	+	0.995618i	$0.470191\pi$
$368$		0			0
$369$	−2.67145	−	4.40708i	−0.139070	−	0.229424i
$370$		0			0
$371$	1.73684	−	1.85324i	0.0901722	−	0.0962152i
$372$		0			0
$373$	11.5793	−	20.0559i	0.599551	−	1.03845i	−0.393336	−	0.919395i	$-0.628679\pi$
$373$	11.5793	−	20.0559i	0.599551	−	1.03845i	0.992887	−	0.119058i	$-0.0379876\pi$
$374$		0			0
$375$	−20.5416	+	0.219262i	−1.06076	+	0.0113226i
$376$		0			0
$377$	−12.8428			−0.661437
$378$		0			0
$379$	−22.7259			−1.16735			−0.583676	−	0.811987i	$-0.698386\pi$
$379$	−22.7259			−1.16735			−0.583676	+	0.811987i	$0.698386\pi$
$380$		0			0
$381$	−32.2242	+	0.343962i	−1.65089	+	0.0176217i
$382$		0			0
$383$	11.6021	−	20.0954i	0.592837	−	1.02682i	−0.401011	−	0.916073i	$-0.631341\pi$
$383$	11.6021	−	20.0954i	0.592837	−	1.02682i	0.993848	−	0.110751i	$-0.0353257\pi$
$384$		0			0
$385$	−21.0766	−	4.92136i	−1.07416	−	0.250816i
$386$		0			0
$387$	14.7890	−	26.9267i	0.751765	−	1.36876i
$388$		0			0
$389$	4.56737	+	7.91091i	0.231575	+	0.401099i	0.958272	−	0.285859i	$-0.0922789\pi$
$389$	4.56737	+	7.91091i	0.231575	+	0.401099i	−0.726697	+	0.686958i	$0.758946\pi$
$390$		0			0
$391$	15.5637	+	26.9572i	0.787092	+	1.36328i
$392$		0			0
$393$	−11.5089	+	20.4346i	−0.580546	+	1.03079i
$394$		0			0
$395$	−5.16881	+	8.95265i	−0.260071	+	0.450456i
$396$		0			0
$397$	−19.2126	−	33.2773i	−0.964255	−	1.67014i	−0.711603	−	0.702582i	$-0.752031\pi$
$397$	−19.2126	−	33.2773i	−0.964255	−	1.67014i	−0.252652	−	0.967557i	$-0.581303\pi$
$398$		0			0
$399$	−0.0885182	−	0.281282i	−0.00443145	−	0.0140817i
$400$		0			0
$401$	−1.47348	+	2.55214i	−0.0735821	+	0.127448i	−0.900469	−	0.434921i	$-0.856776\pi$
$401$	−1.47348	+	2.55214i	−0.0735821	+	0.127448i	0.826887	+	0.562369i	$0.190110\pi$
$402$		0			0
$403$	−1.81598	−	3.14537i	−0.0904603	−	0.156682i
$404$		0			0
$405$	6.58571	−	12.6221i	0.327247	−	0.627197i
$406$		0			0
$407$	−4.55478	+	7.88912i	−0.225772	+	0.391049i
$408$		0			0
$409$	6.60591			0.326641			0.163321	−	0.986573i	$-0.447779\pi$
$409$	6.60591			0.326641			0.163321	+	0.986573i	$0.447779\pi$
$410$		0			0
$411$	12.1202	+	20.4848i	0.597848	+	1.01044i
$412$		0			0
$413$	−24.0473	−	5.61503i	−1.18329	−	0.276297i
$414$		0			0
$415$	−8.04638	−	13.9367i	−0.394981	−	0.684127i
$416$		0			0
$417$	11.9832	+	20.2531i	0.586818	+	0.991798i
$418$		0			0
$419$	0.381961	+	0.661576i	0.0186600	+	0.0323201i	0.875205	−	0.483753i	$-0.160727\pi$
$419$	0.381961	+	0.661576i	0.0186600	+	0.0323201i	−0.856545	+	0.516073i	$0.827393\pi$
$420$		0			0
$421$	−2.48798	+	4.30931i	−0.121257	+	0.210023i	−0.920264	−	0.391299i	$-0.872026\pi$
$421$	−2.48798	+	4.30931i	−0.121257	+	0.210023i	0.799007	+	0.601322i	$0.205359\pi$
$422$		0			0
$423$	−15.6215	+	0.333526i	−0.759542	+	0.0162166i
$424$		0			0
$425$	−11.5283			−0.559204
$426$		0			0
$427$	−37.0757	−	8.65713i	−1.79422	−	0.418948i
$428$		0			0
$429$	−5.99533	+	10.6450i	−0.289457	+	0.513946i
$430$		0			0
$431$	4.01856	−	6.96035i	0.193567	−	0.335268i	−0.752863	−	0.658178i	$-0.771328\pi$
$431$	4.01856	−	6.96035i	0.193567	−	0.335268i	0.946430	+	0.322909i	$0.104661\pi$
$432$		0			0
$433$	−10.8006			−0.519043			−0.259522	−	0.965737i	$-0.583565\pi$
$433$	−10.8006			−0.519043			−0.259522	+	0.965737i	$0.583565\pi$
$434$		0			0
$435$	13.1368	+	22.2028i	0.629860	+	1.06454i
$436$		0			0
$437$	−0.433963			−0.0207593
$438$		0			0
$439$	20.1194			0.960244			0.480122	−	0.877202i	$-0.340592\pi$
$439$	20.1194			0.960244			0.480122	+	0.877202i	$0.340592\pi$
$440$		0			0
$441$	19.0227	+	8.89588i	0.905843	+	0.423613i
$442$		0			0
$443$	9.21245			0.437697			0.218848	−	0.975759i	$-0.429770\pi$
$443$	9.21245			0.437697			0.218848	+	0.975759i	$0.429770\pi$
$444$		0			0
$445$	−13.0463			−0.618455
$446$		0			0
$447$	5.06636	−	8.99558i	0.239631	−	0.425476i
$448$		0			0
$449$	−22.4840			−1.06109			−0.530544	−	0.847658i	$-0.678012\pi$
$449$	−22.4840			−1.06109			−0.530544	+	0.847658i	$0.678012\pi$
$450$		0			0
$451$	4.44183	−	7.69347i	0.209158	−	0.362271i
$452$		0			0
$453$	−7.53342	−	12.7325i	−0.353951	−	0.598223i
$454$		0			0
$455$	5.55902	+	1.29803i	0.260611	+	0.0608524i
$456$		0			0
$457$	18.7955			0.879218			0.439609	−	0.898189i	$-0.355117\pi$
$457$	18.7955			0.879218			0.439609	+	0.898189i	$0.355117\pi$
$458$		0			0
$459$	11.3206	−	21.1435i	0.528401	−	0.986896i
$460$		0			0
$461$	10.3773	−	17.9739i	0.483317	−	0.837129i	−0.516500	−	0.856287i	$-0.672765\pi$
$461$	10.3773	−	17.9739i	0.483317	−	0.837129i	0.999816	+	0.0191582i	$0.00609862\pi$
$462$		0			0
$463$	−10.0414	−	17.3922i	−0.466663	−	0.808284i	0.532612	−	0.846360i	$-0.321211\pi$
$463$	−10.0414	−	17.3922i	−0.466663	−	0.808284i	−0.999275	+	0.0380753i	$0.987877\pi$
$464$		0			0
$465$	−3.58022	+	6.35686i	−0.166029	+	0.294792i
$466$		0			0
$467$	−14.6015	−	25.2905i	−0.675676	−	1.17030i	−0.976271	−	0.216553i	$-0.930519\pi$
$467$	−14.6015	−	25.2905i	−0.675676	−	1.17030i	0.300595	−	0.953752i	$-0.402815\pi$
$468$		0			0
$469$	−32.2006	−	7.51880i	−1.48689	−	0.347186i
$470$		0			0
$471$	4.57221	−	0.0488039i	0.210676	−	0.00224876i
$472$		0			0
$473$	52.9563			2.43493
$474$		0			0
$475$	0.0803606	−	0.139189i	0.00368720	−	0.00638642i
$476$		0			0
$477$	−1.38642	+	2.52430i	−0.0634798	+	0.115580i
$478$		0			0
$479$	−20.0327	−	34.6977i	−0.915319	−	1.58538i	−0.806434	−	0.591324i	$-0.798606\pi$
$479$	−20.0327	−	34.6977i	−0.915319	−	1.58538i	−0.108884	−	0.994054i	$-0.534728\pi$
$480$		0			0
$481$	1.20134	−	2.08078i	0.0547763	−	0.0948754i
$482$		0			0
$483$	20.8914	−	22.7738i	0.950591	−	1.03625i
$484$		0			0
$485$	11.4945	+	19.9091i	0.521939	+	0.904024i
$486$		0			0
$487$	−9.32801	+	16.1566i	−0.422692	+	0.732125i	−0.996202	−	0.0870742i	$-0.972248\pi$
$487$	−9.32801	+	16.1566i	−0.422692	+	0.732125i	0.573509	+	0.819199i	$0.305582\pi$
$488$		0			0
$489$	−15.6619	−	26.4706i	−0.708254	−	1.19704i
$490$		0			0
$491$	0.285132	+	0.493864i	0.0128678	+	0.0222878i	0.872388	−	0.488815i	$-0.162571\pi$
$491$	0.285132	+	0.493864i	0.0128678	+	0.0222878i	−0.859520	+	0.511102i	$0.829237\pi$
$492$		0			0
$493$	21.7297	+	37.6370i	0.978657	+	1.69508i
$494$		0			0
$495$	24.5359	−	0.523853i	1.10281	−	0.0235454i
$496$		0			0
$497$	−11.5724	−	2.70213i	−0.519092	−	0.121207i
$498$		0			0
$499$	−0.464297	+	0.804185i	−0.0207848	+	0.0360003i	−0.876231	−	0.481892i	$-0.839950\pi$
$499$	−0.464297	+	0.804185i	−0.0207848	+	0.0360003i	0.855446	+	0.517892i	$0.173283\pi$
$500$		0			0
$501$	7.03713	+	11.8937i	0.314396	+	0.531370i
$502$		0			0
$503$	3.27170			0.145878			0.0729389	−	0.997336i	$-0.476762\pi$
$503$	3.27170			0.145878			0.0729389	+	0.997336i	$0.476762\pi$
$504$		0			0
$505$	−9.88071			−0.439686
$506$		0			0
$507$	−9.46827	+	16.8114i	−0.420501	+	0.746620i
$508$		0			0
$509$	−4.48391	+	7.76635i	−0.198746	+	0.344238i	−0.948122	−	0.317907i	$-0.897020\pi$
$509$	−4.48391	+	7.76635i	−0.198746	+	0.344238i	0.749376	+	0.662144i	$0.230353\pi$
$510$		0			0
$511$	3.40733	−	3.63567i	0.150731	−	0.160833i
$512$		0			0
$513$	0.176367	+	0.284067i	0.00778680	+	0.0125419i
$514$		0			0
$515$	4.56974	+	7.91502i	0.201367	+	0.348778i
$516$		0			0
$517$	−13.4672	−	23.3258i	−0.592286	−	1.02587i
$518$		0			0
$519$	−13.2727	+	0.141673i	−0.582605	+	0.00621874i
$520$		0			0
$521$	−5.37649	+	9.31235i	−0.235548	+	0.407982i	−0.959432	−	0.281940i	$-0.909022\pi$
$521$	−5.37649	+	9.31235i	−0.235548	+	0.407982i	0.723884	+	0.689922i	$0.242355\pi$
$522$		0			0
$523$	16.2796	+	28.1970i	0.711856	+	1.23297i	0.964160	+	0.265322i	$0.0854784\pi$
$523$	16.2796	+	28.1970i	0.711856	+	1.23297i	−0.252304	+	0.967648i	$0.581188\pi$
$524$		0			0
$525$	3.43581	+	10.9179i	0.149951	+	0.476496i
$526$		0			0
$527$	−6.14519	+	10.6438i	−0.267689	+	0.463650i
$528$		0			0
$529$	−11.2404	−	19.4690i	−0.488714	−	0.846477i
$530$		0			0
$531$	27.9942	−	0.597690i	1.21484	−	0.0259375i
$532$		0			0
$533$	−1.17155	+	2.02918i	−0.0507453	+	0.0878935i
$534$		0			0
$535$	0.794500			0.0343492
$536$		0			0
$537$	20.0361	−	35.5751i	0.864622	−	1.53518i
$538$		0			0
$539$	2.34486	+	36.1237i	0.101000	+	1.55596i
$540$		0			0
$541$	−3.46359	−	5.99911i	−0.148911	−	0.257922i	0.781914	−	0.623386i	$-0.214244\pi$
$541$	−3.46359	−	5.99911i	−0.148911	−	0.257922i	−0.930825	+	0.365464i	$0.880910\pi$
$542$		0			0
$543$	−30.0840	+	0.321118i	−1.29103	+	0.0137805i
$544$		0			0
$545$	3.75250	+	6.49952i	0.160739	+	0.278409i
$546$		0			0
$547$	15.8974	−	27.5351i	0.679725	−	1.17732i	−0.295339	−	0.955392i	$-0.595433\pi$
$547$	15.8974	−	27.5351i	0.679725	−	1.17732i	0.975064	−	0.221925i	$-0.0712340\pi$
$548$		0			0
$549$	43.1609	−	0.921505i	1.84206	−	0.0393289i
$550$		0			0
$551$	−0.605888			−0.0258117
$552$		0			0
$553$	16.8372	+	3.93147i	0.715990	+	0.167183i
$554$		0			0
$555$	−4.82613	+	0.0515142i	−0.204858	+	0.00218666i
$556$		0			0
$557$	14.1679	−	24.5395i	0.600314	−	1.03977i	−0.392460	−	0.919769i	$-0.628376\pi$
$557$	14.1679	−	24.5395i	0.600314	−	1.03977i	0.992773	−	0.120005i	$-0.0382909\pi$
$558$		0			0
$559$	−13.9674			−0.590758
$560$		0			0
$561$	41.3402	−	0.441266i	1.74538	−	0.0186303i
$562$		0			0
$563$	44.6541			1.88194			0.940972	−	0.338484i	$-0.109914\pi$
$563$	44.6541			1.88194			0.940972	+	0.338484i	$0.109914\pi$
$564$		0			0
$565$	−3.52213			−0.148177
$566$		0			0
$567$	−23.3980	−	4.41974i	−0.982623	−	0.185612i
$568$		0			0
$569$	−21.2205			−0.889608			−0.444804	−	0.895628i	$-0.646727\pi$
$569$	−21.2205			−0.889608			−0.444804	+	0.895628i	$0.646727\pi$
$570$		0			0
$571$	−11.8957			−0.497820			−0.248910	−	0.968527i	$-0.580072\pi$
$571$	−11.8957			−0.497820			−0.248910	+	0.968527i	$0.580072\pi$
$572$		0			0
$573$	8.39407	−	0.0895985i	0.350667	−	0.00374303i
$574$		0			0
$575$	16.8442			0.702450
$576$		0			0
$577$	−19.3490	+	33.5135i	−0.805511	+	1.39519i	0.110435	+	0.993883i	$0.464776\pi$
$577$	−19.3490	+	33.5135i	−0.805511	+	1.39519i	−0.915946	+	0.401302i	$0.868558\pi$
$578$		0			0
$579$	25.3589	−	0.270682i	1.05388	−	0.0112491i
$580$		0			0
$581$	−18.4056	+	19.6391i	−0.763593	+	0.814766i
$582$		0			0
$583$	−4.96449			−0.205608
$584$		0			0
$585$	−6.47142	+	0.138168i	−0.267560	+	0.00571254i
$586$		0			0
$587$	−9.92138	+	17.1843i	−0.409499	+	0.709274i	−0.994834	−	0.101518i	$-0.967630\pi$
$587$	−9.92138	+	17.1843i	−0.409499	+	0.709274i	0.585334	+	0.810792i	$0.300963\pi$
$588$		0			0
$589$	−0.0856730	−	0.148390i	−0.00353010	−	0.00611431i
$590$		0			0
$591$	33.2528	−	0.354941i	1.36784	−	0.0146003i
$592$		0			0
$593$	10.9566	+	18.9774i	0.449933	+	0.779307i	0.998381	−	0.0568775i	$-0.0181144\pi$
$593$	10.9566	+	18.9774i	0.449933	+	0.779307i	−0.548448	+	0.836185i	$0.684781\pi$
$594$		0			0
$595$	−5.60176	−	18.4875i	−0.229650	−	0.757912i
$596$		0			0
$597$	11.0631	−	19.6431i	0.452782	−	0.803938i
$598$		0			0
$599$	−33.0445			−1.35016			−0.675081	−	0.737743i	$-0.735892\pi$
$599$	−33.0445			−1.35016			−0.675081	+	0.737743i	$0.735892\pi$
$600$		0			0
$601$	11.4951	−	19.9100i	0.468893	−	0.812147i	−0.530475	−	0.847701i	$-0.677986\pi$
$601$	11.4951	−	19.9100i	0.468893	−	0.812147i	0.999368	+	0.0355541i	$0.0113196\pi$
$602$		0			0
$603$	37.4856	−	0.800336i	1.52653	−	0.0325922i
$604$		0			0
$605$	12.4519	+	21.5674i	0.506242	+	0.876838i
$606$		0			0
$607$	13.8282	−	23.9511i	0.561269	−	0.972146i	−0.436118	−	0.899890i	$-0.643647\pi$
$607$	13.8282	−	23.9511i	0.561269	−	0.972146i	0.997386	−	0.0722559i	$-0.0230198\pi$
$608$		0			0
$609$	29.1680	−	31.7963i	1.18195	−	1.28845i
$610$		0			0
$611$	3.55201	+	6.15226i	0.143699	+	0.248894i
$612$		0			0
$613$	−15.7684	+	27.3116i	−0.636879	+	1.10311i	0.349235	+	0.937035i	$0.386442\pi$
$613$	−15.7684	+	27.3116i	−0.636879	+	1.10311i	−0.986114	+	0.166072i	$0.946892\pi$
$614$		0			0
$615$	4.70645	−	0.0502367i	0.189782	−	0.00202574i
$616$		0			0
$617$	−10.7513	−	18.6217i	−0.432830	−	0.749683i	0.564286	−	0.825580i	$-0.309152\pi$
$617$	−10.7513	−	18.6217i	−0.432830	−	0.749683i	−0.997116	+	0.0758961i	$0.975818\pi$
$618$		0			0
$619$	14.1261	+	24.4671i	0.567776	+	0.983417i	0.996785	+	0.0801169i	$0.0255294\pi$
$619$	14.1261	+	24.4671i	0.567776	+	0.983417i	−0.429009	+	0.903300i	$0.641137\pi$
$620$		0			0
$621$	−16.5407	+	30.8932i	−0.663756	+	1.23970i
$622$		0			0
$623$	6.32759	+	20.8829i	0.253509	+	0.836656i
$624$		0			0
$625$	3.13665	−	5.43283i	0.125466	−	0.217313i
$626$		0			0
$627$	−0.282844	+	0.502204i	−0.0112957	+	0.0200561i
$628$		0			0
$629$	−8.13056			−0.324187
$630$		0			0
$631$	9.12550			0.363281			0.181640	−	0.983365i	$-0.441859\pi$
$631$	9.12550			0.363281			0.181640	+	0.983365i	$0.441859\pi$
$632$		0			0
$633$	−13.1132	−	22.1630i	−0.521202	−	0.880899i
$634$		0			0
$635$	14.7159	−	25.4888i	0.583985	−	1.01149i
$636$		0			0
$637$	−0.618464	−	9.52774i	−0.0245044	−	0.377503i
$638$		0			0
$639$	13.4717	−	0.287628i	0.532933	−	0.0113784i
$640$		0			0
$641$	−16.4489	−	28.4904i	−0.649693	−	1.12530i	−0.983196	−	0.182552i	$-0.941564\pi$
$641$	−16.4489	−	28.4904i	−0.649693	−	1.12530i	0.333503	−	0.942749i	$-0.391769\pi$
$642$		0			0
$643$	−10.1276	−	17.5415i	−0.399392	−	0.691767i	0.594259	−	0.804274i	$-0.297445\pi$
$643$	−10.1276	−	17.5415i	−0.399392	−	0.691767i	−0.993651	+	0.112506i	$0.964112\pi$
$644$		0			0
$645$	14.2871	+	24.1471i	0.562554	+	0.950790i
$646$		0			0
$647$	5.67441	−	9.82837i	0.223084	−	0.386393i	−0.732659	−	0.680596i	$-0.761721\pi$
$647$	5.67441	−	9.82837i	0.223084	−	0.386393i	0.955743	+	0.294203i	$0.0950542\pi$
$648$		0			0
$649$	24.1336	+	41.8007i	0.947328	+	1.64082i
$650$		0			0
$651$	11.9117	+	2.64762i	0.466857	+	0.103769i
$652$		0			0
$653$	−1.79018	+	3.10069i	−0.0700552	+	0.121339i	−0.898925	−	0.438102i	$-0.855651\pi$
$653$	−1.79018	+	3.10069i	−0.0700552	+	0.121339i	0.828870	+	0.559441i	$0.188984\pi$
$654$		0			0
$655$	−10.7096	−	18.5496i	−0.418459	−	0.724792i
$656$		0			0
$657$	−2.71988	+	4.95217i	−0.106113	+	0.193203i
$658$		0			0
$659$	−9.13582	+	15.8237i	−0.355881	+	0.616404i	−0.987268	−	0.159064i	$-0.949152\pi$
$659$	−9.13582	+	15.8237i	−0.355881	+	0.616404i	0.631387	+	0.775468i	$0.282486\pi$
$660$		0			0
$661$	2.23391			0.0868891			0.0434446	−	0.999056i	$-0.486167\pi$
$661$	2.23391			0.0868891			0.0434446	+	0.999056i	$0.486167\pi$
$662$		0			0
$663$	−10.9036	+	0.116385i	−0.423461	+	0.00452003i
$664$		0			0
$665$	0.262260	+	0.0612374i	0.0101700	+	0.00237468i
$666$		0			0
$667$	−31.7496	−	54.9919i	−1.22935	−	2.12930i
$668$		0			0
$669$	19.0536	−	33.8307i	0.736655	−	1.30797i
$670$		0			0
$671$	37.2087	+	64.4474i	1.43643	+	2.48797i
$672$		0			0
$673$	−12.4804	+	21.6166i	−0.481083	+	0.833260i	−0.999764	−	0.0217074i	$-0.993090\pi$
$673$	−12.4804	+	21.6166i	−0.481083	+	0.833260i	0.518681	+	0.854968i	$0.326423\pi$
$674$		0			0
$675$	−6.84565	−	11.0260i	−0.263489	−	0.424391i
$676$		0			0
$677$	−19.8127			−0.761463			−0.380731	−	0.924686i	$-0.624328\pi$
$677$	−19.8127			−0.761463			−0.380731	+	0.924686i	$0.624328\pi$
$678$		0			0
$679$	26.2930	−	28.0551i	1.00903	−	1.07665i
$680$		0			0
$681$	−3.43489	−	5.80541i	−0.131625	−	0.222464i
$682$		0			0
$683$	−5.72871	+	9.92242i	−0.219203	+	0.379671i	−0.954565	−	0.298004i	$-0.903679\pi$
$683$	−5.72871	+	9.92242i	−0.219203	+	0.379671i	0.735361	+	0.677675i	$0.237012\pi$
$684$		0			0
$685$	−21.7381			−0.830571
$686$		0			0
$687$	−1.17905	+	2.09346i	−0.0449835	+	0.0798705i
$688$		0			0
$689$	1.30940			0.0498842
$690$		0			0
$691$	−40.5105			−1.54109			−0.770545	−	0.637385i	$-0.780016\pi$
$691$	−40.5105			−1.54109			−0.770545	+	0.637385i	$0.780016\pi$
$692$		0			0
$693$	−12.7387	−	39.0199i	−0.483901	−	1.48224i
$694$		0			0
$695$	−21.4922			−0.815247
$696$		0			0
$697$	7.92893			0.300330
$698$		0			0
$699$	−15.8591	−	26.8040i	−0.599847	−	1.01382i
$700$		0			0
$701$	−29.5416			−1.11577			−0.557885	−	0.829918i	$-0.688387\pi$
$701$	−29.5416			−1.11577			−0.557885	+	0.829918i	$0.688387\pi$
$702$		0			0
$703$	0.0566760	−	0.0981657i	0.00213758	−	0.00370239i
$704$		0			0
$705$	7.00283	−	12.4339i	0.263742	−	0.468287i
$706$		0			0
$707$	4.79224	+	15.8158i	0.180231	+	0.594814i
$708$		0			0
$709$	−37.4814			−1.40764			−0.703822	−	0.710376i	$-0.748525\pi$
$709$	−37.4814			−1.40764			−0.703822	+	0.710376i	$0.748525\pi$
$710$		0			0
$711$	−19.6007	+	0.418484i	−0.735082	+	0.0156944i
$712$		0			0
$713$	8.97883	−	15.5518i	0.336260	−	0.582419i
$714$		0			0
$715$	−5.57897	−	9.66306i	−0.208642	−	0.361378i
$716$		0			0
$717$	−4.72820	−	7.99127i	−0.176578	−	0.298439i
$718$		0			0
$719$	−6.35418	−	11.0058i	−0.236971	−	0.410445i	0.722873	−	0.690981i	$-0.242821\pi$
$719$	−6.35418	−	11.0058i	−0.236971	−	0.410445i	−0.959844	+	0.280536i	$0.909488\pi$
$720$		0			0
$721$	10.4530	−	11.1535i	0.389290	−	0.415379i
$722$		0			0
$723$	0.367429	+	0.621002i	0.0136648	+	0.0230953i
$724$		0			0
$725$	23.5174			0.873414
$726$		0			0
$727$	−19.9463	+	34.5480i	−0.739768	+	1.28132i	0.212832	+	0.977089i	$0.431731\pi$
$727$	−19.9463	+	34.5480i	−0.739768	+	1.28132i	−0.952600	+	0.304227i	$0.901602\pi$
$728$		0			0
$729$	26.9447	−	1.72794i	0.997950	−	0.0639979i
$730$		0			0
$731$	23.6325	+	40.9327i	0.874080	+	1.51395i
$732$		0			0
$733$	22.4091	−	38.8137i	0.827699	−	1.43362i	−0.0721400	−	0.997395i	$-0.522983\pi$
$733$	22.4091	−	38.8137i	0.827699	−	1.43362i	0.899839	−	0.436222i	$-0.143684\pi$
$734$		0			0
$735$	−15.8391	+	10.8150i	−0.584234	+	0.398919i
$736$		0			0
$737$	32.3162	+	55.9732i	1.19038	+	2.06180i
$738$		0			0
$739$	6.64954	−	11.5173i	0.244607	−	0.423672i	−0.717414	−	0.696647i	$-0.754674\pi$
$739$	6.64954	−	11.5173i	0.244607	−	0.423672i	0.962021	+	0.272975i	$0.0880076\pi$
$740$		0			0
$741$	0.0746010	−	0.132458i	0.00274054	−	0.00486596i
$742$		0			0
$743$	−2.15562	−	3.73365i	−0.0790822	−	0.136974i	0.823772	−	0.566921i	$-0.191866\pi$
$743$	−2.15562	−	3.73365i	−0.0790822	−	0.136974i	−0.902854	+	0.429947i	$0.858532\pi$
$744$		0			0
$745$	4.71451	+	8.16578i	0.172726	+	0.299171i
$746$		0			0
$747$	14.6922	−	26.7505i	0.537558	−	0.978749i
$748$		0			0
$749$	−0.385340	−	1.27174i	−0.0140800	−	0.0464682i
$750$		0			0
$751$	−21.7651	+	37.6983i	−0.794221	+	1.37563i	0.129112	+	0.991630i	$0.458787\pi$
$751$	−21.7651	+	37.6983i	−0.794221	+	1.37563i	−0.923333	+	0.384001i	$0.874546\pi$
$752$		0			0
$753$	39.0739	−	0.417076i	1.42393	−	0.0151991i
$754$		0			0
$755$	13.5115			0.491733
$756$		0			0
$757$	34.6790			1.26043			0.630215	−	0.776420i	$-0.282967\pi$
$757$	34.6790			1.26043			0.630215	+	0.776420i	$0.282967\pi$
$758$		0			0
$759$	−60.4028	+	0.644741i	−2.19248	+	0.0234026i
$760$		0			0
$761$	1.75973	−	3.04794i	0.0637902	−	0.110488i	−0.832367	−	0.554226i	$-0.813014\pi$
$761$	1.75973	−	3.04794i	0.0637902	−	0.110488i	0.896157	+	0.443738i	$0.146348\pi$
$762$		0			0
$763$	8.58362	−	9.15886i	0.310748	−	0.331573i
$764$		0			0
$765$	11.3544	+	18.7313i	0.410520	+	0.677232i
$766$		0			0
$767$	−6.36533	−	11.0251i	−0.229839	−	0.398092i
$768$		0			0
$769$	−19.5075	−	33.7879i	−0.703457	−	1.21842i	−0.967245	−	0.253843i	$-0.918305\pi$
$769$	−19.5075	−	33.7879i	−0.703457	−	1.21842i	0.263788	−	0.964581i	$-0.415028\pi$
$770$		0			0
$771$	−9.38884	+	16.6704i	−0.338131	+	0.600369i
$772$		0			0
$773$	23.2169	−	40.2128i	0.835054	−	1.44636i	−0.0589329	−	0.998262i	$-0.518770\pi$
$773$	23.2169	−	40.2128i	0.835054	−	1.44636i	0.893987	−	0.448094i	$-0.147897\pi$
$774$		0			0
$775$	3.32538	+	5.75972i	0.119451	+	0.206895i
$776$		0			0
$777$	2.42318	+	7.70008i	0.0869310	+	0.276239i
$778$		0			0
$779$	−0.0552705	+	0.0957313i	−0.00198027	+	0.00342993i
$780$		0			0
$781$	11.6139	+	20.1159i	0.415578	+	0.719802i
$782$		0			0
$783$	−23.0937	+	43.1323i	−0.825303	+	1.54142i
$784$		0			0
$785$	−2.08801	+	3.61654i	−0.0745242	+	0.129080i
$786$		0			0
$787$	−47.4424			−1.69114			−0.845569	−	0.533866i	$-0.820739\pi$
$787$	−47.4424			−1.69114			−0.845569	+	0.533866i	$0.820739\pi$
$788$		0			0
$789$	22.4572	+	37.9555i	0.799496	+	1.35125i
$790$		0			0
$791$	1.70827	+	5.63778i	0.0607390	+	0.200456i
$792$		0			0
$793$	−9.81393	−	16.9982i	−0.348503	−	0.603625i
$794$		0			0
$795$	−1.33937	−	2.26371i	−0.0475027	−	0.0802857i
$796$		0			0
$797$	7.69773	+	13.3329i	0.272668	+	0.472274i	0.969544	−	0.244917i	$-0.0787607\pi$
$797$	7.69773	+	13.3329i	0.272668	+	0.472274i	−0.696876	+	0.717191i	$0.745427\pi$
$798$		0			0
$799$	12.0198	−	20.8190i	0.425232	−	0.736523i
$800$		0			0
$801$	−12.8256	−	21.1583i	−0.453171	−	0.747593i
$802$		0			0
$803$	−9.73932			−0.343693
$804$		0			0
$805$	8.18482	+	27.0123i	0.288477	+	0.952059i
$806$		0			0
$807$	−4.74208	+	8.41981i	−0.166929	+	0.296391i
$808$		0			0
$809$	−15.0433	+	26.0557i	−0.528893	+	0.916069i	0.470539	+	0.882379i	$0.344059\pi$
$809$	−15.0433	+	26.0557i	−0.528893	+	0.916069i	−0.999432	+	0.0336903i	$0.989274\pi$
$810$		0			0
$811$	11.2821			0.396170			0.198085	−	0.980185i	$-0.436528\pi$
$811$	11.2821			0.396170			0.198085	+	0.980185i	$0.436528\pi$
$812$		0			0
$813$	−2.58678	−	4.37200i	−0.0907224	−	0.153333i
$814$		0			0
$815$	28.0902			0.983955
$816$		0			0
$817$	−0.658944			−0.0230535
$818$		0			0
$819$	3.35986	+	10.2916i	0.117403	+	0.359618i
$820$		0			0
$821$	3.25266			0.113519			0.0567593	−	0.998388i	$-0.481923\pi$
$821$	3.25266			0.113519			0.0567593	+	0.998388i	$0.481923\pi$
$822$		0			0
$823$	−14.5968			−0.508814			−0.254407	−	0.967097i	$-0.581880\pi$
$823$	−14.5968			−0.508814			−0.254407	+	0.967097i	$0.581880\pi$
$824$		0			0
$825$	10.9785	−	19.4929i	0.382223	−	0.678656i
$826$		0			0
$827$	−42.7500			−1.48656			−0.743282	−	0.668978i	$-0.766732\pi$
$827$	−42.7500			−1.48656			−0.743282	+	0.668978i	$0.766732\pi$
$828$		0			0
$829$	−17.6799	+	30.6225i	−0.614049	+	1.06356i	0.376502	+	0.926416i	$0.377127\pi$
$829$	−17.6799	+	30.6225i	−0.614049	+	1.06356i	−0.990551	+	0.137148i	$0.956207\pi$
$830$		0			0
$831$	19.4846	+	32.9314i	0.675912	+	1.14238i
$832$		0			0
$833$	−26.8755	+	17.9332i	−0.931180	+	0.621348i
$834$		0			0
$835$	−12.6214			−0.436780
$836$		0			0
$837$	−13.8291	+	0.442972i	−0.478005	+	0.0153114i
$838$		0			0
$839$	−15.0886	+	26.1343i	−0.520917	+	0.902255i	0.478787	+	0.877931i	$0.341077\pi$
$839$	−15.0886	+	26.1343i	−0.520917	+	0.902255i	−0.999704	+	0.0243242i	$0.992257\pi$
$840$		0			0
$841$	−29.8280	−	51.6637i	−1.02855	−	1.78151i
$842$		0			0
$843$	4.77696	−	8.48173i	0.164527	−	0.292126i
$844$		0			0
$845$	−8.81072	−	15.2606i	−0.303098	−	0.524981i
$846$		0			0
$847$	28.4830	−	30.3918i	0.978688	−	1.04428i
$848$		0			0
$849$	36.8911	−	0.393777i	1.26610	−	0.0135144i
$850$		0			0
$851$	11.8797			0.407230
$852$		0			0
$853$	−20.4789	+	35.4705i	−0.701184	+	1.21449i	0.266867	+	0.963733i	$0.414011\pi$
$853$	−20.4789	+	35.4705i	−0.701184	+	1.21449i	−0.968051	+	0.250753i	$0.919322\pi$
$854$		0			0
$855$	−0.305304	+	0.00651839i	−0.0104412	+	0.000222924i
$856$		0			0
$857$	−15.2283	−	26.3762i	−0.520190	−	0.900995i	−0.999724	−	0.0234720i	$-0.992528\pi$
$857$	−15.2283	−	26.3762i	−0.520190	−	0.900995i	0.479535	−	0.877523i	$-0.340805\pi$
$858$		0			0
$859$	1.59467	−	2.76206i	0.0544096	−	0.0942401i	−0.837538	−	0.546379i	$-0.816006\pi$
$859$	1.59467	−	2.76206i	0.0544096	−	0.0942401i	0.891947	+	0.452139i	$0.149339\pi$
$860$		0			0
$861$	−2.36308	−	7.50912i	−0.0805337	−	0.255910i
$862$		0			0
$863$	−11.5498	−	20.0049i	−0.393161	−	0.680975i	0.599703	−	0.800222i	$-0.295285\pi$
$863$	−11.5498	−	20.0049i	−0.393161	−	0.680975i	−0.992865	+	0.119247i	$0.961952\pi$
$864$		0			0
$865$	6.06128	−	10.4984i	0.206090	−	0.356958i
$866$		0			0
$867$	3.79598	+	6.41570i	0.128918	+	0.217889i
$868$		0			0
$869$	−16.8976	−	29.2675i	−0.573212	−	0.992833i
$870$		0			0
$871$	−8.52349	−	14.7631i	−0.288808	−	0.500229i
$872$		0			0
$873$	−20.9882	+	38.2139i	−0.710344	+	1.29335i
$874$		0			0
$875$	−30.5576	−	7.13517i	−1.03304	−	0.241213i
$876$		0			0
$877$	1.64469	−	2.84868i	0.0555372	−	0.0961932i	−0.836920	−	0.547325i	$-0.815646\pi$
$877$	1.64469	−	2.84868i	0.0555372	−	0.0961932i	0.892457	+	0.451132i	$0.148980\pi$
$878$		0			0
$879$	−24.8945	−	42.0750i	−0.839672	−	1.41915i
$880$		0			0
$881$	51.4835			1.73452			0.867262	−	0.497852i	$-0.165878\pi$
$881$	51.4835			1.73452			0.867262	+	0.497852i	$0.165878\pi$
$882$		0			0
$883$	−0.359433			−0.0120959			−0.00604794	−	0.999982i	$-0.501925\pi$
$883$	−0.359433			−0.0120959			−0.00604794	+	0.999982i	$0.501925\pi$
$884$		0			0
$885$	−12.5493	+	22.2819i	−0.421840	+	0.748999i
$886$		0			0
$887$	5.79998	−	10.0459i	0.194744	−	0.337307i	−0.752072	−	0.659080i	$-0.770946\pi$
$887$	5.79998	−	10.0459i	0.194744	−	0.337307i	0.946817	+	0.321774i	$0.104279\pi$
$888$		0			0
$889$	−47.9366	−	11.1931i	−1.60774	−	0.375406i
$890$		0			0
$891$	24.9704	+	39.2770i	0.836540	+	1.31583i
$892$		0			0
$893$	0.167574	+	0.290247i	0.00560767	+	0.00971276i
$894$		0			0
$895$	18.6446	+	32.2935i	0.623222	+	1.07945i
$896$		0			0
$897$	15.9314	−	0.170053i	0.531935	−	0.00567789i
$898$		0			0
$899$	12.5360	−	21.7130i	0.418100	−	0.724170i
$900$		0			0
$901$	−2.21548	−	3.83732i	−0.0738082	−	0.127840i
$902$		0			0
$903$	31.7222	−	34.5806i	1.05565	−	1.15077i
$904$		0			0
$905$	13.7386	−	23.7960i	0.456686	−	0.791004i
$906$		0			0
$907$	12.2895	+	21.2861i	0.408067	+	0.706793i	0.994673	−	0.103079i	$-0.0328695\pi$
$907$	12.2895	+	21.2861i	0.408067	+	0.706793i	−0.586606	+	0.809873i	$0.699536\pi$
$908$		0			0
$909$	−9.71356	−	16.0244i	−0.322179	−	0.531496i
$910$		0			0
$911$	20.1678	−	34.9317i	0.668190	−	1.15734i	−0.310219	−	0.950665i	$-0.600402\pi$
$911$	20.1678	−	34.9317i	0.668190	−	1.15734i	0.978410	−	0.206675i	$-0.0662642\pi$
$912$		0			0
$913$	52.6096			1.74112
$914$		0			0
$915$	−19.3483	+	34.3538i	−0.639634	+	1.13570i
$916$		0			0
$917$	−24.4976	+	26.1393i	−0.808981	+	0.863197i
$918$		0			0
$919$	−10.8377	−	18.7714i	−0.357501	−	0.619210i	0.630041	−	0.776562i	$-0.283038\pi$
$919$	−10.8377	−	18.7714i	−0.357501	−	0.619210i	−0.987543	+	0.157351i	$0.949705\pi$
$920$		0			0
$921$	−4.17970	+	0.0446143i	−0.137726	+	0.00147009i
$922$		0			0
$923$	−3.06320	−	5.30562i	−0.100827	−	0.174637i
$924$		0			0
$925$	−2.19986	+	3.81028i	−0.0723311	+	0.125281i
$926$		0			0
$927$	−8.34405	+	15.1923i	−0.274055	+	0.498980i
$928$		0			0
$929$	−7.92818			−0.260115			−0.130058	−	0.991506i	$-0.541516\pi$
$929$	−7.92818			−0.260115			−0.130058	+	0.991506i	$0.541516\pi$
$930$		0			0
$931$	−0.0291775	−	0.449493i	−0.000956254	−	0.0147316i
$932$		0			0
$933$	16.5173	−	0.176306i	0.540751	−	0.00577199i
$934$		0			0
$935$	−18.8790	+	32.6994i	−0.617409	+	1.06938i
$936$		0			0
$937$	5.84549			0.190964			0.0954819	−	0.995431i	$-0.469561\pi$
$937$	5.84549			0.190964			0.0954819	+	0.995431i	$0.469561\pi$
$938$		0			0
$939$	−56.4650	+	0.602709i	−1.84267	+	0.0196687i
$940$		0			0
$941$	−39.0091			−1.27166			−0.635831	−	0.771829i	$-0.719342\pi$
$941$	−39.0091			−1.27166			−0.635831	+	0.771829i	$0.719342\pi$
$942$		0			0
$943$	−11.5851			−0.377262
$944$		0			0
$945$	14.3556	−	16.3358i	0.466987	−	0.531403i
$946$		0			0
$947$	7.04371			0.228890			0.114445	−	0.993430i	$-0.463491\pi$
$947$	7.04371			0.228890			0.114445	+	0.993430i	$0.463491\pi$
$948$		0			0
$949$	2.56878			0.0833861
$950$		0			0
$951$	5.36826	−	0.0573009i	0.174078	−	0.00185811i
$952$		0			0
$953$	28.2379			0.914716			0.457358	−	0.889283i	$-0.348796\pi$
$953$	28.2379			0.914716			0.457358	+	0.889283i	$0.348796\pi$
$954$		0			0
$955$	−3.83336	+	6.63957i	−0.124044	+	0.214851i
$956$		0			0
$957$	−84.3329	+	0.900172i	−2.72610	+	0.0290984i
$958$		0			0
$959$	10.5432	+	34.7957i	0.340458	+	1.12361i
$960$		0			0
$961$	−23.9096			−0.771277
$962$		0			0
$963$	0.781059	+	1.28851i	0.0251693	+	0.0415216i
$964$		0			0
$965$	−11.5808	+	20.0585i	−0.372798	+	0.645705i
$966$		0			0
$967$	0.430925	+	0.746384i	0.0138576	+	0.0240021i	0.872871	−	0.487951i	$-0.162256\pi$
$967$	0.430925	+	0.746384i	0.0138576	+	0.0240021i	−0.859013	+	0.511953i	$0.828922\pi$
$968$		0			0
$969$	−0.514403	+	0.00549075i	−0.0165250	+	0.000176388i
$970$		0			0
$971$	19.6403	+	34.0181i	0.630288	+	1.09169i	0.987493	+	0.157665i	$0.0503967\pi$
$971$	19.6403	+	34.0181i	0.630288	+	1.09169i	−0.357204	+	0.934026i	$0.616270\pi$
$972$		0			0
$973$	10.4239	+	34.4021i	0.334176	+	1.10288i
$974$		0			0
$975$	−2.89562	+	5.14132i	−0.0927340	+	0.164654i
$976$		0			0
$977$	−34.5478			−1.10528			−0.552641	−	0.833419i	$-0.686380\pi$
$977$	−34.5478			−1.10528			−0.552641	+	0.833419i	$0.686380\pi$
$978$		0			0
$979$	21.3252	−	36.9363i	0.681555	−	1.18049i
$980$		0			0
$981$	−6.85182	+	12.4753i	−0.218762	+	0.398307i
$982$		0			0
$983$	−10.0096	−	17.3372i	−0.319258	−	0.552971i	0.661076	−	0.750319i	$-0.270100\pi$
$983$	−10.0096	−	17.3372i	−0.319258	−	0.552971i	−0.980333	+	0.197349i	$0.936767\pi$
$984$		0			0
$985$	−15.1857	+	26.3024i	−0.483856	+	0.838063i
$986$		0			0
$987$	−23.2990	−	5.17869i	−0.741616	−	0.164840i
$988$		0			0
$989$	−34.5298	−	59.8074i	−1.09798	−	1.90177i
$990$		0			0
$991$	−2.27853	+	3.94653i	−0.0723799	+	0.125366i	−0.899944	−	0.436006i	$-0.856393\pi$
$991$	−2.27853	+	3.94653i	−0.0723799	+	0.125366i	0.827564	+	0.561371i	$0.189726\pi$
$992$		0			0
$993$	−6.36752	+	0.0679670i	−0.202067	+	0.00215687i
$994$		0			0
$995$	10.2948	+	17.8311i	0.326367	+	0.565284i
$996$		0			0
$997$	−10.8662	−	18.8207i	−0.344135	−	0.596059i	0.641061	−	0.767490i	$-0.278494\pi$
$997$	−10.8662	−	18.8207i	−0.344135	−	0.596059i	−0.985196	+	0.171431i	$0.945161\pi$
$998$		0			0
$999$	−4.82803	−	7.77631i	−0.152752	−	0.246032i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.q.k.529.1		22
3.2	odd	2		3024.2.q.k.2881.5		22
4.3	odd	2		504.2.q.d.25.11	✓	22
7.2	even	3		1008.2.t.k.961.8		22
9.4	even	3		1008.2.t.k.193.8		22
9.5	odd	6		3024.2.t.l.1873.7		22
12.11	even	2		1512.2.q.c.1369.5		22
21.2	odd	6		3024.2.t.l.289.7		22
28.23	odd	6		504.2.t.d.457.4	yes	22
36.23	even	6		1512.2.t.d.361.7		22
36.31	odd	6		504.2.t.d.193.4	yes	22
63.23	odd	6		3024.2.q.k.2305.5		22
63.58	even	3	inner	1008.2.q.k.625.1		22
84.23	even	6		1512.2.t.d.289.7		22
252.23	even	6		1512.2.q.c.793.5		22
252.247	odd	6		504.2.q.d.121.11	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.11	✓	22	4.3	odd	2
504.2.q.d.121.11	yes	22	252.247	odd	6
504.2.t.d.193.4	yes	22	36.31	odd	6
504.2.t.d.457.4	yes	22	28.23	odd	6
1008.2.q.k.529.1		22	1.1	even	1	trivial
1008.2.q.k.625.1		22	63.58	even	3	inner
1008.2.t.k.193.8		22	9.4	even	3
1008.2.t.k.961.8		22	7.2	even	3
1512.2.q.c.793.5		22	252.23	even	6
1512.2.q.c.1369.5		22	12.11	even	2
1512.2.t.d.289.7		22	84.23	even	6
1512.2.t.d.361.7		22	36.23	even	6
3024.2.q.k.2305.5		22	63.23	odd	6
3024.2.q.k.2881.5		22	3.2	odd	2
3024.2.t.l.289.7		22	21.2	odd	6
3024.2.t.l.1873.7		22	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.73195 + 0.0184869i) q^{3} +(0.790938 - 1.36994i) q^{5} +(-2.57645 - 0.601597i) q^{7} +(2.99932 - 0.0640368i) q^{9} +O(q^{10})\)	\(q+(-1.73195 + 0.0184869i) q^{3} +(0.790938 - 1.36994i) q^{5} +(-2.57645 - 0.601597i) q^{7} +(2.99932 - 0.0640368i) q^{9} +(2.58569 + 4.47855i) q^{11} +(-0.681985 - 1.18123i) q^{13} +(-1.34454 + 2.38730i) q^{15} +(-2.30781 + 3.99724i) q^{17} +(-0.0321742 - 0.0557274i) q^{19} +(4.47341 + 0.994307i) q^{21} +(3.37197 - 5.84043i) q^{23} +(1.24883 + 2.16305i) q^{25} +(-5.19349 + 0.166357i) q^{27} +(4.70787 - 8.15427i) q^{29} +2.66278 q^{31} +(-4.56109 - 7.70884i) q^{33} +(-2.86196 + 3.05376i) q^{35} +(0.880766 + 1.52553i) q^{37} +(1.20300 + 2.03323i) q^{39} +(-0.858924 - 1.48770i) q^{41} +(5.12012 - 8.86831i) q^{43} +(2.28455 - 4.15955i) q^{45} -5.20834 q^{47} +(6.27616 + 3.09997i) q^{49} +(3.92312 - 6.96569i) q^{51} +(-0.479996 + 0.831377i) q^{53} +8.18049 q^{55} +(0.0567545 + 0.0959224i) q^{57} +9.33353 q^{59} +14.3902 q^{61} +(-7.76611 - 1.63939i) q^{63} -2.15763 q^{65} +12.4981 q^{67} +(-5.73213 + 10.1777i) q^{69} +4.49160 q^{71} +(-0.941655 + 1.63099i) q^{73} +(-2.20291 - 3.72320i) q^{75} +(-3.96762 - 13.0943i) q^{77} -6.53504 q^{79} +(8.99180 - 0.384134i) q^{81} +(5.08661 - 8.81026i) q^{83} +(3.65066 + 6.32314i) q^{85} +(-8.00306 + 14.2098i) q^{87} +(-4.12369 - 7.14243i) q^{89} +(1.04647 + 3.45366i) q^{91} +(-4.61181 + 0.0492266i) q^{93} -0.101791 q^{95} +(-7.26638 + 12.5857i) q^{97} +(8.04210 + 13.2670i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 2 q^{3} + 3 q^{5} + 5 q^{7} + 10 q^{9}+O(q^{10}) \) 22 * q - 2 * q^3 + 3 * q^5 + 5 * q^7 + 10 * q^9	\( 22 q - 2 q^{3} + 3 q^{5} + 5 q^{7} + 10 q^{9} + 3 q^{11} - 3 q^{13} + q^{15} + 7 q^{17} + q^{19} - 2 q^{23} - 10 q^{25} + 4 q^{27} + 9 q^{29} - 8 q^{31} + 29 q^{33} - 14 q^{35} + 2 q^{37} + 16 q^{39} + 16 q^{41} + q^{45} + 10 q^{47} + 15 q^{49} - 7 q^{51} + 11 q^{53} - 22 q^{55} + 7 q^{57} - 38 q^{59} + 26 q^{61} - 48 q^{63} - 26 q^{65} + 52 q^{67} - 4 q^{69} + 48 q^{71} - 35 q^{73} + 23 q^{75} + 17 q^{77} + 20 q^{79} - 38 q^{81} + 28 q^{83} - 20 q^{85} + 33 q^{87} + 6 q^{89} + 37 q^{91} + 19 q^{93} + 24 q^{95} - 29 q^{97} + 56 q^{99}+O(q^{100}) \) 22 * q - 2 * q^3 + 3 * q^5 + 5 * q^7 + 10 * q^9 + 3 * q^11 - 3 * q^13 + q^15 + 7 * q^17 + q^19 - 2 * q^23 - 10 * q^25 + 4 * q^27 + 9 * q^29 - 8 * q^31 + 29 * q^33 - 14 * q^35 + 2 * q^37 + 16 * q^39 + 16 * q^41 + q^45 + 10 * q^47 + 15 * q^49 - 7 * q^51 + 11 * q^53 - 22 * q^55 + 7 * q^57 - 38 * q^59 + 26 * q^61 - 48 * q^63 - 26 * q^65 + 52 * q^67 - 4 * q^69 + 48 * q^71 - 35 * q^73 + 23 * q^75 + 17 * q^77 + 20 * q^79 - 38 * q^81 + 28 * q^83 - 20 * q^85 + 33 * q^87 + 6 * q^89 + 37 * q^91 + 19 * q^93 + 24 * q^95 - 29 * q^97 + 56 * q^99

Introduction

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